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import sys
from rpython.rlib.rarithmetic import ovfcheck, LONG_BIT, maxint, is_valid_int
from rpython.rlib.objectmodel import we_are_translated
from rpython.rtyper.lltypesystem import lltype
from rpython.rtyper.lltypesystem.lloperation import llop
from rpython.jit.metainterp.resoperation import rop, ResOperation
from rpython.jit.metainterp.optimizeopt.info import AbstractInfo, INFO_NONNULL,\
INFO_UNKNOWN, INFO_NULL
from rpython.jit.metainterp.history import ConstInt
MAXINT = maxint
MININT = -maxint - 1
IS_64_BIT = sys.maxint > 2**32
def next_pow2_m1(n):
"""Calculate next power of 2 greater than n minus one."""
n |= n >> 1
n |= n >> 2
n |= n >> 4
n |= n >> 8
n |= n >> 16
if IS_64_BIT:
n |= n >> 32
return n
class IntBound(AbstractInfo):
_attrs_ = ('upper', 'lower')
def __init__(self, lower, upper):
self.upper = upper
self.lower = lower
# check for unexpected overflows:
if not we_are_translated():
assert type(upper) is not long or is_valid_int(upper)
assert type(lower) is not long or is_valid_int(lower)
# Returns True if the bound was updated
def make_le(self, other):
return self.make_le_const(other.upper)
def make_le_const(self, other):
if other < self.upper:
self.upper = other
return True
return False
def make_lt(self, other):
return self.make_lt_const(other.upper)
def make_lt_const(self, other):
try:
other = ovfcheck(other - 1)
except OverflowError:
return False
return self.make_le_const(other)
def make_ge(self, other):
return self.make_ge_const(other.lower)
def make_ge_const(self, other):
if other > self.lower:
self.lower = other
return True
return False
def make_gt_const(self, other):
try:
other = ovfcheck(other + 1)
except OverflowError:
return False
return self.make_ge_const(other)
def make_eq_const(self, intval):
self.upper = intval
self.lower = intval
def make_ne_const(self, intval):
if self.lower < intval == self.upper:
self.upper -= 1
return True
if self.lower == intval < self.upper:
self.lower += 1
return True
return False
def make_gt(self, other):
return self.make_gt_const(other.lower)
def is_constant(self):
return self.lower == self.upper
def get_constant_int(self):
assert self.is_constant()
return self.lower
def equal(self, value):
if not self.is_constant():
return False
return self.lower == value
def known_lt_const(self, other):
return self.upper < other
def known_le_const(self, other):
return self.upper <= other
def known_gt_const(self, other):
return self.lower > other
def known_ge_const(self, other):
return self.lower >= other
def known_lt(self, other):
return self.known_lt_const(other.lower)
def known_le(self, other):
return self.known_le_const(other.lower)
def known_gt(self, other):
return other.known_lt(self)
def known_ge(self, other):
return other.known_le(self)
def known_nonnegative(self):
return 0 <= self.lower
def intersect(self, other):
from rpython.jit.metainterp.optimize import InvalidLoop
if self.known_gt(other) or self.known_lt(other):
# they don't overlap, which makes the loop invalid
# this never happens in regular linear traces, but it can happen in
# combination with unrolling/loop peeling
raise InvalidLoop("two integer ranges don't overlap")
r = False
if self.make_ge_const(other.lower):
r = True
if self.make_le_const(other.upper):
r = True
return r
def intersect_const(self, lower, upper):
r = self.make_ge_const(lower)
if self.make_le_const(upper):
r = True
return r
def add_bound(self, other):
""" add two bounds. must be correct even in the presence of possible
overflows. """
try:
lower = ovfcheck(self.lower + other.lower)
except OverflowError:
return IntUnbounded()
try:
upper = ovfcheck(self.upper + other.upper)
except OverflowError:
return IntUnbounded()
return IntBound(lower, upper)
def add_bound_cannot_overflow(self, other):
""" returns True if self + other can never overflow """
try:
ovfcheck(self.upper + other.upper)
ovfcheck(self.lower + other.lower)
except OverflowError:
return False
return True
def add_bound_no_overflow(self, other):
""" return the bound that self + other must have, if no overflow occured,
eg after an int_add_ovf(...), guard_no_overflow() """
lower = MININT
try:
lower = ovfcheck(self.lower + other.lower)
except OverflowError:
pass
upper = MAXINT
try:
upper = ovfcheck(self.upper + other.upper)
except OverflowError:
pass
return IntBound(lower, upper)
def sub_bound(self, other):
try:
lower = ovfcheck(self.lower - other.upper)
except OverflowError:
return IntUnbounded()
try:
upper = ovfcheck(self.upper - other.lower)
except OverflowError:
return IntUnbounded()
return IntBound(lower, upper)
def sub_bound_cannot_overflow(self, other):
try:
ovfcheck(self.lower - other.upper)
ovfcheck(self.upper - other.lower)
except OverflowError:
return False
return True
def sub_bound_no_overflow(self, other):
lower = MININT
try:
lower = ovfcheck(self.lower - other.upper)
except OverflowError:
pass
upper = MAXINT
try:
upper = ovfcheck(self.upper - other.lower)
except OverflowError:
pass
return IntBound(lower, upper)
def mul_bound(self, other):
try:
vals = (ovfcheck(self.upper * other.upper),
ovfcheck(self.upper * other.lower),
ovfcheck(self.lower * other.upper),
ovfcheck(self.lower * other.lower))
return IntBound(min4(vals), max4(vals))
except OverflowError:
return IntUnbounded()
mul_bound_no_overflow = mul_bound # can be improved
def mul_bound_cannot_overflow(self, other):
try:
ovfcheck(self.upper * other.upper)
ovfcheck(self.upper * other.lower)
ovfcheck(self.lower * other.upper)
ovfcheck(self.lower * other.lower)
except OverflowError:
return False
return True
def py_div_bound(self, other):
if not other.contains(0):
try:
# this gives the bounds for 'int_py_div', so use the
# Python-style handling of negative numbers and not
# the C-style one
vals = (ovfcheck(self.upper / other.upper),
ovfcheck(self.upper / other.lower),
ovfcheck(self.lower / other.upper),
ovfcheck(self.lower / other.lower))
return IntBound(min4(vals), max4(vals))
except OverflowError:
pass
return IntUnbounded()
def mod_bound(self, other):
r = IntUnbounded()
if other.is_constant():
val = other.get_constant_int()
if val >= 0: # with Python's modulo: 0 <= (x % pos) < pos
r.make_ge_const(0)
r.make_lt_const(val)
else: # with Python's modulo: neg < (x % neg) <= 0
r.make_gt_const(val)
r.make_le_const(0)
return r
def lshift_bound(self, other):
if other.known_nonnegative() and \
other.known_lt_const(LONG_BIT):
try:
vals = (ovfcheck(self.upper << other.upper),
ovfcheck(self.upper << other.lower),
ovfcheck(self.lower << other.upper),
ovfcheck(self.lower << other.lower))
return IntBound(min4(vals), max4(vals))
except (OverflowError, ValueError):
pass
return IntUnbounded()
def lshift_bound_cannot_overflow(self, other):
if other.known_nonnegative() and \
other.known_lt_const(LONG_BIT):
try:
ovfcheck(self.upper << other.upper)
ovfcheck(self.upper << other.lower)
ovfcheck(self.lower << other.upper)
ovfcheck(self.lower << other.lower)
return True
except (OverflowError, ValueError):
pass
return False
def rshift_bound(self, other):
if other.known_nonnegative() and \
other.known_lt_const(LONG_BIT):
vals = (self.upper >> other.upper,
self.upper >> other.lower,
self.lower >> other.upper,
self.lower >> other.lower)
return IntBound(min4(vals), max4(vals))
else:
return IntUnbounded()
def and_bound(self, other):
pos1 = self.known_nonnegative()
pos2 = other.known_nonnegative()
r = IntUnbounded()
if pos1 or pos2:
r.make_ge_const(0)
if pos1:
r.make_le(self)
if pos2:
r.make_le(other)
return r
def or_bound(self, other):
r = IntUnbounded()
if self.known_nonnegative() and \
other.known_nonnegative():
mostsignificant = self.upper | other.upper
r.intersect(IntBound(0, next_pow2_m1(mostsignificant)))
return r
def invert_bound(self):
upper = ~self.lower
lower = ~self.upper
return IntBound(lower, upper)
def neg_bound(self):
try:
upper = ovfcheck(-self.lower)
except OverflowError:
return IntUnbounded()
try:
lower = ovfcheck(-self.upper)
except OverflowError:
return IntUnbounded()
return IntBound(lower, upper)
def contains(self, val):
if not we_are_translated():
assert not isinstance(val, long)
if not isinstance(val, int):
if (self.lower == MININT and self.upper == MAXINT):
return True # workaround for address as int
if val < self.lower:
return False
if val > self.upper:
return False
return True
def contains_bound(self, other):
assert isinstance(other, IntBound)
if not self.contains(other.lower):
return False
if not self.contains(other.upper):
return False
return True
def __repr__(self):
return '%d <= x <= %u' % (self.lower, self.upper)
def clone(self):
res = IntBound(self.lower, self.upper)
return res
def make_guards(self, box, guards, optimizer):
if self.is_constant():
guards.append(ResOperation(rop.GUARD_VALUE,
[box, ConstInt(self.upper)]))
return
if self.lower > MININT:
bound = self.lower
op = ResOperation(rop.INT_GE, [box, ConstInt(bound)])
guards.append(op)
op = ResOperation(rop.GUARD_TRUE, [op])
guards.append(op)
if self.upper < MAXINT:
bound = self.upper
op = ResOperation(rop.INT_LE, [box, ConstInt(bound)])
guards.append(op)
op = ResOperation(rop.GUARD_TRUE, [op])
guards.append(op)
def is_bool(self):
return (self.known_nonnegative() and
self.known_le_const(1))
def make_bool(self):
self.intersect(IntBound(0, 1))
def getconst(self):
if not self.is_constant():
raise Exception("not a constant")
return ConstInt(self.get_constant_int())
def getnullness(self):
if self.known_gt_const(0) or \
self.known_lt_const(0):
return INFO_NONNULL
if self.known_nonnegative() and \
self.known_le_const(0):
return INFO_NULL
return INFO_UNKNOWN
def widen(self):
info = self.clone()
info.widen_update()
return info
def widen_update(self):
if self.lower < MININT / 2:
self.lower = MININT
if self.upper > MAXINT / 2:
self.upper = MAXINT
def IntUpperBound(upper):
b = IntBound(lower=MININT, upper=upper)
return b
def IntLowerBound(lower):
b = IntBound(upper=MAXINT, lower=lower)
return b
def IntUnbounded():
return IntBound(MININT, MAXINT)
def ConstIntBound(value):
return IntBound(value, value)
def min4(t):
return min(min(t[0], t[1]), min(t[2], t[3]))
def max4(t):
return max(max(t[0], t[1]), max(t[2], t[3]))
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